Abstract Wavelength-shifting (WLS) fiber scintillator detectors were successfully installed at two neutron powder diffractometers at the Spallation Neutron Source (SNS). However, they have the following second-order disadvantages: (i) they cannot have both high efficiency and images free of ghosting (position misassignment) concurrently; (ii) the apparent detection efficiency and spatial resolution are not uniform. These issues are related to the diffusion of scintillation photons and the fluctuation in the number of photons (quantum noise) collected by photo-multiplier tubes (PMTs). To mitigate these two issues, we developed two statistics-based positioning algorithms, i.e., a centroid algorithm (CEA) and a correlation algorithm (CA). Compared with the generally used maximum-photon algorithm (MPA), the CEA eliminates the ghosting with only about a 10% loss in detection efficiency, and provides better uniformity in detection efficiency and intrinsic background and lower gamma-ray sensitivity. The CA can effectively eliminate ghosting too, but the loss of efficiency at the group boundaries of PMTs is large. The results indicate that both algorithms can reduce the influence of quantum noise on the neutron positioning.